This is realism-talk, not gameplay-talk again,
Strategic resources, in the game, serve to limit access to a relatively small number of higher-units, in order to foster conflict and interaction over control of those resources, with the possibility of losing access to those units as the forfeit if you cannot secure them
Lumber would not do that. Lumber, even if just required for shipbuilding, would block access to an entire category of unit and an entire aspect (naval ops) of the game. This is a much higher cost than losing, say, iron (which only enables two infantry and two cavalry units, while leaving other accessible) and prevent interaction with a very large part of the map. If you factor the role of timber (to this day) in construction and argue that many buildings and districts and improvements should require it as well, the situation gets far worse.
That - the fact that it has no more benefits than the other strategic resources while having a criminally higher penalty for those who lack it, is why lumber is different and should not be added, from a gameplay perspective, as a strategic resource. It's simply too ubiquitous a resource for a model that essentially represent *scarce* resources,
At least, not a civ 6 one. A civ IV style strategic resource like stone or marble were, which is not REQUIRED to build anything but accelerate the building of many things, would work much better.